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Solve the differential equation $-y\cdot dx+4x\cdot dy=x^2dx$

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Solution

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Final answer to the problem

$y=\left(\frac{\sqrt[4]{x^{7}}}{7}+C_0\right)\sqrt[4]{x}$
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Step-by-step Solution

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  • Exact Differential Equation
  • Linear Differential Equation
  • Separable Differential Equation
  • Homogeneous Differential Equation
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1

Group the terms of the equation

Learn how to solve differential calculus problems step by step online.

$4x\cdot dy=x^2dx+y\cdot dx$

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Unlock the first 3 steps of this solution

Learn how to solve differential calculus problems step by step online. Solve the differential equation -ydx+4xdy=x^2dx. Group the terms of the equation. Factor the polynomial x^2dx+y\cdot dx by it's greatest common factor (GCF): dx. Grouping the terms of the differential equation. Divide both sides of the equation by dx.

Final answer to the problem

$y=\left(\frac{\sqrt[4]{x^{7}}}{7}+C_0\right)\sqrt[4]{x}$

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Solving a math problem using different methods is important because it enhances understanding, encourages critical thinking, allows for multiple solutions, and develops problem-solving strategies. Read more

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Function Plot

Plotting: $-y\cdot dx+4x\cdot dy-x^2dx$

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Go!
1
2
3
4
5
6
7
8
9
0
a
b
c
d
f
g
m
n
u
v
w
x
y
z
.
(◻)
+
-
×
◻/◻
/
÷
◻2
◻◻
√◻
√

◻√◻
◻√
∞
e
π
ln
log
log◻
lim
d/dx
D□x
∫
∫◻
|◻|
θ
=
>
<
>=
<=
sin
cos
tan
cot
sec
csc

asin
acos
atan
acot
asec
acsc

sinh
cosh
tanh
coth
sech
csch

asinh
acosh
atanh
acoth
asech
acsch

How to improve your answer:

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Main Topic: Differential Calculus

The derivative of a function of a real variable measures the sensitivity to change of a quantity (a function value or dependent variable) which is determined by another quantity (the independent variable). Derivatives are a fundamental tool of calculus.

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